24,902 research outputs found
KRYLOV SUBSPACE METHODS FOR SOLVING LARGE LYAPUNOV EQUATIONS
Published versio
Polynomially filtered exact diagonalization approach to many-body localization
Polynomially filtered exact diagonalization method (POLFED) for large sparse
matrices is introduced. The algorithm finds an optimal basis of a subspace
spanned by eigenvectors with eigenvalues close to a specified energy target by
a spectral transformation using a high order polynomial of the matrix. The
memory requirements scale better with system size than in the state-of-the-art
shift-invert approach. The potential of POLFED is demonstrated examining
many-body localization transition in 1D interacting quantum spin-1/2 chains. We
investigate the disorder strength and system size scaling of Thouless time.
System size dependence of bipartite entanglement entropy and of the gap ratio
highlights the importance of finite-size effects in the system. We discuss
possible scenarios regarding the many-body localization transition obtaining
estimates for the critical disorder strength.Comment: 4+5 pages, version accepted in Physical Review Letters, comments
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Diffusion in sparse networks: linear to semi-linear crossover
We consider random networks whose dynamics is described by a rate equation,
with transition rates that form a symmetric matrix. The long time
evolution of the system is characterized by a diffusion coefficient . In one
dimension it is well known that can display an abrupt percolation-like
transition from diffusion () to sub-diffusion (D=0). A question arises
whether such a transition happens in higher dimensions. Numerically can be
evaluated using a resistor network calculation, or optionally it can be deduced
from the spectral properties of the system. Contrary to a recent expectation
that is based on a renormalization-group analysis, we deduce that is
finite; suggest an "effective-range-hopping" procedure to evaluate it; and
contrast the results with the linear estimate. The same approach is useful for
the analysis of networks that are described by quasi-one-dimensional sparse
banded matrices.Comment: 13 pages, 4 figures, proofed as publishe
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